The odds of getting an Arcane in explore are about 1 in 17, but due to luck, you can go a long time without getting one. Odds of getting an arcane in any other mode is 1/3 of the Explore odds, so significantly more likely to go a long stretch without one.

If you went 4 straight hours, even at 1 minute per match, without a single Arcane, that would be some epic bad luck, though I’ve gone at least 2 or 3 hours (over several days) without getting one. I also got 3 arcanes in 4 matches once last week.

4-5 hours with a team (bombats) that completes each match in under 20-30 seconds

Something’s not quite right.

I’ll take your average numbers at face value: 25 seconds per match for 4.5 hours. Assuming a lot of loading time between games, I’ll round it WAY UP to 45 seconds per game, or 80 Explorers per hour. So that’s 360 Explore battles without a single Arcane Traitstone?

Please take a quick video of it with special focus on the pre battle selection screen.

Here is my tracking data. I've only been tracking Arcanes: First 10 arcanes before tracking but I switched to assassin class before doing exploring at 0 battles in assassin class and 0 of the needed arcane Arcane 11 - 198 Arcane 12 - 230 Arcane 13...

This seems to be the last word on the subject. Before Explore mode, accepted wisdom was that an Arcane would drop about 2% of the time, and with the Explore multiplier, that was modified to 6%. Sirrian himself commented on the original poster’s sample, which supports that this number is at least in the ballpark.

My current personally recorded numbers for Arcanes from Explore are 154 stones out of 2648 battles total (I hit a stretch of terrible luck for a time, enough to skew the final percentage a bit even over the huge amount of battles). Currently just over 5.7%, and trending upward over the last 10 stones. 6% seems in the ballpark. I believe @Rasper had some data as well.

Devs have never come out and stated the drop rate (also stating they never would give specifics), but there was one comment by Sirrian in the linked thread that the numbers in the original post (3.68% drop rate for arcanes) were “unusually low”.

All this is, of course, on PC/Mobile. The drop rates should be the same on console, but I have no way to verify or test that.